本帖最后由 敬畏数学 于 2020-7-14 21:52 编辑
首先,$ \vv{AP} =2m\vv{AB}+(3-2m)\vv{AC},$得:$ \frac{|AP|}{|AD|}=3 ,$由$ (\vv{AP})^2=81,$得:$m=0$或者$m=\frac{27}{25} ,$且$ \vv{AD}=\frac{1}{3}\vv{AP}$,$ \vv{CD}=\vv{CA}+\vv{AD} =\frac{2}{3}m\vv{AB}-\frac{2}{3}m\vv{AC}$,两边平方得:$ CD $长度为0或者$ \frac{18}{5} $.也可以这样:$ \vv{CB}=K\vv{CD} ,\vv{AP}=2m\vv{CB}+3\vv{AC}=\vv{AC}+\vv{CP},\vv{CP}=2mk\vv{CD}-2\vv{CA},2mk=3,CD=\frac{CB}{K}=\frac{18}{5},0r,CD=0$ |